Inclusive and Exclusive Compton Processes in Quantum Chromodynamics

1.8 MB·English

by  Ales Psaker

INCLUSIVE AND EXCLUSIVE COMPTON PROCESSES
IN QUANTUM CHROMODYNAMICS
by
A. Psaker
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0 B.S. March 1997, University of Ljubljana
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M.S. May 2001, Old Dominion University
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a
J

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A Dissertation Submitted to the Faculty of

2 Old Dominion University in Partial Fulfillment of the
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3 Requirement for the Degree of
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1 DOCTOR OF PHILOSOPHY
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0 PHYSICS
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- OLD DOMINION UNIVERSITY
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December 2005
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r Approved by:
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Anatoly Radyushkin (Director)
Ian Balitsky
Charles Hyde-Wright
Mark Havey
John Adam
ABSTRACT
INCLUSIVE AND EXCLUSIVE COMPTON PROCESSES
IN QUANTUM CHROMODYNAMICS
A. Psaker
Old Dominion University, 2008
Director: Dr. Anatoly Radyushkin
In our work, we describe two types of Compton processes. As an example of an inclu-
sive process, we consider the high-energy photoproduction of massive muon pairs off
the nucleon. We analyze the process in the framework of the QCD parton model, in
which the usual parton distributions emerge as a toolto describe the nucleon in terms
of quark and gluonic degrees of freedom. To study its exclusive version, a new class
of phenomenological functions is required, namely, generalized parton distributions.
They can be considered as a generalization of the usual parton distributions mea-
sured in deeply inelastic lepton-nucleon scattering. Generalized parton distributions
(GPDs) may be observed in hard exclusive reactions such as deeply virtual Compton
scattering. We develop an extension of this particular process into the weak inter-
action sector. We also investigate a possible application of the GPD formalism to
wide-angle real Compton scattering.
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c Copyright, 2008, by A. Psaker, All Rights Reserved.
(cid:13)
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ACKNOWLEDGMENTS
I would like to express sincere and deep gratitude to my advisor Anatoly Radyushkin
for his generous support and guidance during my graduate student years. I would
like to extend my gratitude to all the members of my committee for their helpful
comments and suggestions. In particular, I’m grateful to Charles Hyde-Wright and
Wally Melnitchouk for various stimulating and valuable discussions. I would like to
thank my colleagues at the Physics Department of Old Dominion University and
the Theory Group of Jefferson Lab. I’m thankful to my family for their support,
and to my wife Mateja for her patience and continuous encouragement. This work
was supported by the US Department of Energy DE-FG02-97ER41028 and by the
contract DE-AC05-84ER40150 under which the Southeastern Universities Research
Association (SURA) operates the Thomas Jefferson Accelerator Facility.
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TABLE OF CONTENTS
Page
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
CHAPTER
I Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II Deeply Inelastic Lepton Scattering . . . . . . . . . . . . . . . . . . . . . 5
II.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
II.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
II.3 Bjorken Scaling and the Parton Model . . . . . . . . . . . . . . . . 12
III Phenomenological Functions . . . . . . . . . . . . . . . . . . . . . . . . . 17
III.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
III.2 Form Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
III.3 Parton Distribution Functions . . . . . . . . . . . . . . . . . . . . . 19
III.4 Distribution Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . 22
III.5 Generalized Parton Distributions . . . . . . . . . . . . . . . . . . . 23
III.5.1 Skewed Parton Distributions . . . . . . . . . . . . . . . . . . 24
III.5.2 Double Distributions . . . . . . . . . . . . . . . . . . . . . . 29
IV Deeply Virtual Compton Scattering . . . . . . . . . . . . . . . . . . . . . 32
IV.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
IV.2 Virtual Compton Scattering Amplitude . . . . . . . . . . . . . . . . 33
IV.3 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
IV.4 Toy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
IV.5 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
V Inclusive Photoproduction of Lepton Pairs . . . . . . . . . . . . . . . . . 57
V.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
V.2 Compton Subprocess . . . . . . . . . . . . . . . . . . . . . . . . . . 58
V.3 Bethe-Heitler Subprocess . . . . . . . . . . . . . . . . . . . . . . . . 64
V.4 Interference Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
V.5 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
VI Exclusive Photoproduction of Lepton Pairs . . . . . . . . . . . . . . . . . 75
VI.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
VI.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
VI.3 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
VI.3.1 Compton Process . . . . . . . . . . . . . . . . . . . . . . . . 79
VI.3.2 Bethe-Heitler Process . . . . . . . . . . . . . . . . . . . . . . 83
VII Weak Deeply Virtual Compton Scattering . . . . . . . . . . . . . . . . . 89
VII.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
VII.2 Weak Virtual Compton Scattering Amplitude . . . . . . . . . . . . 90
VII.2.1 Weak Neutral Amplitude . . . . . . . . . . . . . . . . . . . . 91
VII.2.2 Weak Charged Amplitude . . . . . . . . . . . . . . . . . . . 94
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VII.3 Weak DVCS Processes . . . . . . . . . . . . . . . . . . . . . . . . . 96
VII.3.1 Weak Neutral Neutrino-Proton Scattering . . . . . . . . . . 97
VII.3.2 Weak Neutral Electron-Proton Scattering . . . . . . . . . . 99
VII.3.3 Weak Charged Neutrino-Neutron Scattering . . . . . . . . . 103
VIII Wide-Angle Real Compton Scattering . . . . . . . . . . . . . . . . . . . 112
VIII.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
VIII.2 Twist Decomposition and Parametrization . . . . . . . . . . . . . . 114
VIII.3 Compton Scattering Amplitude . . . . . . . . . . . . . . . . . . . . 118
VIII.3.1 Twist-2 Amplitude . . . . . . . . . . . . . . . . . . . . . . . 119
VIII.3.2 Twist-3 Amplitude . . . . . . . . . . . . . . . . . . . . . . . 119
VIII.3.3 Electromagnetic Gauge Invariance . . . . . . . . . . . . . . . 121
VIII.3.4 Helicity Amplitudes . . . . . . . . . . . . . . . . . . . . . . 122
VIII.3.5 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
VIII.4 Compton Scattering on a Pion in QED . . . . . . . . . . . . . . . . 131
IX Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
APPENDICES
A Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B List of Integrals and Scalar Functions That Appear in the Bethe-Heitler Subprocess of the Inclusiv
C Modified Parametrization of the Nonforward Matrix Element in the Scalar Toy Model148
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
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LIST OF TABLES
Page
I Lower and upper limits of the invariant momentum transfer t within the kinematically allo
II Polar angles φ and φ′ of the incoming and scattered leptons, respectively, in the target rest
III Polar angles φ and φ′ of the incoming and scattered leptons, respectively, in the target rest
IV Orders of magnitude (in nbarns) for the unpolarized total weak neutral σ , Compton weak
νp
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LIST OF FIGURES
Page
1 Deeply inelastic electron-nucleon scattering in the one-photon exchange approximation.
2 Forward virtual Compton scattering amplitude. . . . . . . . . . . . . 9
3 Kinematics of deeply inelastic electron-nucleon scattering in the parton model. 14
4 Elastic electron-nucleon scattering in the one-photon exchange approximation. 20
5 Deeply inelastic electron-nucleon scattering cross section as the imaginary part of the forw
6 The handbag contribution to the process γ∗γ π0. . . . . . . . . . . 23
→
7 Comparison between the descriptions in terms of nonforward and off-forward parton distribution
8 Handbag contribution to the nonforward virtual Compton scattering amplitude. 27
9 Description in terms of double distributions. . . . . . . . . . . . . . . 30
10 Conversion from a double distribution to an off-forward parton distribution function with
11 DVCS (a) and Bethe-Heitler (b and c) diagrams contributing to electroproduction of a real
12 Handbag diagrams (s- and u-channel) in the virtual Compton scattering amplitude. 34
13 Kinematics of the generalized DVCS process in the target rest frame. 43
14 Kinematically allowed region for sˆ 4 GeV2 and Q2 2.5 GeV2 with ω = 5.75 GeV (solid
≥ 1 ≥
15 Invariant momentum transfer t plotted as a function of the angle θ between the incoming
γγ
16 Compton cross section σ plotted as a function of the angle θ between the incoming virtual
C γγ
17 Bethe-Heitler cross section σ plotted as a function of the angle θ between the incoming
BH γγ
18 Bethe-Heitler cross section σ plotted as a function of the angle θ between the incoming
BH γγ
19 Compton cross section σ (solid line) and Bethe-Heitler cross section σ (dashed line) plotted
C BH
20 Inclusive photoproduction of lepton pairs. . . . . . . . . . . . . . . . 57
21 Compton contribution to the inclusive photoproduction of lepton pairs in the parton model.
22 Bethe-Heitler contribution to the inclusive photoproduction of lepton pairs in the parton mo
23 Bjorken scaling variable x plotted as a function of the angle θ between the incoming real
B γγ
24 Invariant momentum transfer t plotted as a function of the angle θ between the incoming
γγ
25 Unpolarized valence quark distributions for u-flavor (bold solid line) and d-flavor (solid line),
26 Compton cross section σ (solid line) and Bethe-Heitler cross section σ (dashed line) plotted
C BH
27 Exclusive photoproduction of lepton pairs. . . . . . . . . . . . . . . . 76
28 DVCS (a) and Bethe-Heitler (b and c) diagrams contributing to the exclusive photoproduction
29 Invariant momentum transfer t plotted as a function of the angle θ between the incoming
γγ
30 Energy of the scattered nucleon E plotted as a function of the angle θ between the incoming
2 γγ
31 Contributions from u quarks (solid line) and d quarks (dashed line) to the real part of +
HT
32 Contributions from u quarks (solid line) and d quarks (dashed line) to the imaginary part
33 Contributions from u quarks (solid line) and d quarks (dashed line) to the real part of ˜+
HT
34 Contributions from u quarks (solid line) and d quarks (dashed line) to the imaginary part
35 Compton cross section σ plotted as a function of the angle θ between the incoming real
C γγ
36 Bethe-Heitler cross section σ plotted plotted as a function of the angle θ between the
BH γγ
37 Compton cross section σ (solid line) and Bethe-Heitler cross section σ (dashed line) plotted
C BH
38 Handbag diagrams (s- and u-channel) in the weak virtual Compton scattering amplitude.
39 DVCS (a) and Bethe-Heitler (b and c) diagrams in the weak deeply virtual Compton scattering
40 Weak neutral DVCS cross section σ plotted as a function of the angle θ between the incoming
νp Bγ
41 Compton cross section σ for the weak neutral DVCS process plotted as a function of the
Cep
ix
42 Bethe-Heitler cross section σ for the weak neutral DVCS process plotted as a function
BHep
43 Bethe-Heitler cross section σ for the weak neutral DVCS process plotted as a function
BHep
44 Compton cross section σ (solid line) and Bethe-Heitler cross section σ (dashed line)
Cep BHep
45 Compton cross section σ for the weak charged DVCS process plotted as a function of the
Cνn
46 Bethe-Heitler cross section σ for the weak charged DVCS process plotted as a function
BHνn
47 Bethe-Heitler cross section σ for the weak charged DVCS process plotted as a function
BHνn
48 Compton cross section σ (solid line) and Bethe-Heitler cross section σ (dashed line)
Cνn BHνn
49 Handbag contribution (a and b) and the configuration (c) with the exchange of two hard
(1,1) (2,2)
50 Real part of the helicity amplitudes H (solid line) and H (dashed line) plotted
twist−2 twist−2
(1,1) (2,2)
51 Imaginary part of the helicity amplitudes H (solid line) and H (dashed line) plotted
twist−2 twist−2
(1,1) (2,2)
52 Real part of the helicity amplitudes H (solid line) and H (dashed line) plotted
twist−2 twist−2
(1,1) (2,2)
53 Imaginary part of the helicity amplitudes H (solid line) and H (dashed line) plotted
twist−2 twist−2
(1,1) (2,2)
54 Real part of the helicity amplitudes H (solid line) and H (dashed line) plotted
twist−2 twist−2
(1,1) (2,2)
55 Imaginary part of the helicity amplitudes H (solid line) and H (dashed line) plotted
twist−2 twist−2
56 Twist-2 cross section σ(1,1) plotted as a function of the center-of-mass scattering angle θ
cm
57 Twist-2 cross section σ(2,2) plotted as a function of the center-of-mass scattering angle θ
cm
58 Combination s4.6dσ(2,2)/dt plotted as a function of the center-of-mass scattering angle θ
cm
59 Feynman diagrams for Compton scattering on a pion in QED. . . . . 132
1
CHAPTER I
INTRODUCTION
Strong interactionphysics, the study ofhadronstructure ingeneral, is oneofthe most
fascinating frontiers of modern science. The underlying theory is the universally
accepted nonAbelian gauge field theory called quantum chromodynamics (QCD).
In principle, QCD embraces all phenomena of hadronic physics. It postulates that
hadrons (baryons and mesons) are composite objects made up of quarks, and that
the color interaction between quarks is mediated by gluons as the gauge bosons. The
main difficulty of this elegant theory lies in the fact that it is formulated in terms
of colored degrees of freedom (quarks and gluons) while the physical hadrons are
colorless. How the hadrons are built out of quarks and gluons has yet to be answered,
and it represents a challenging task.
Historically, QCD originated from the constituent quark model [1, 2]. In the
1960’s, the development of high-energy accelerators made it possible to resolve the
structure of hadrons for the first time. The studies of the hadron spectroscopy led to
the concept of quarks as the fundamental building blocks of hadrons, in particular,
threequarksforbaryonsandaquark-antiquarkpairformesons. Thenaturalstepthat
followed, was the search for quarks in the experiments with the momentum transfer
large enough to look inside the hadrons. The first series of such high-resolution ex-
periments was performed at SLAC by probing the proton structure. The process was
known as deeply inelastic electron-proton scattering (DIS). It is probably the most
studied QCD process. The data on DIS have strongly supported the parton model, a
physical picture given by Feynman [3, 4, 5], in which the proton, when observed with
high spatial resolution, is built out of almost-free and point-like constituents. They
were called partons. Thus the dynamics of partons described by the QCD parton
model should have the property of asymptotic freedom. In other words, the coupling
constant of interaction between partons is vanishing at small distances (or large mo-
mentum transfers). In addition, the DIS experiments also suggested that charged
partons should be spin-1/2 particles that were later identified with quarks. Another
important result from these experiments was the first evidence for the presence of
This dissertation follows the style of The Physical Review.